Download Statistics Review Chapters 1-8

AP Review #4
1. What is independence?
2. You are going to flip a coin three times. What is the sample space for each flip?
3. You are going to flip a coin three times and note how many heads and tails you get. What is the
sample space?
4. You are going to flip a coin three times and note what you get on each flip. What is the sample
space?
5. Create a tree diagram for the three flips.
6. There are three ways I can drive from Fremont to Grand Rapids and four ways I can drive from Grand
Rapids to my home. How many different ways can I drive from Fremont to my home through Grand
Rapids?
7. How many different four-digit numbers are there?
8. How many different four-digit numbers can you make without repeating digits?
9. If S is the sample space, P(S) = _____.
10. What are complements? Give an example and draw a Venn diagram.
11. What are disjoint events? Give two examples and draw a Venn diagram.
M & M Color
Probability
Brown
0.3
Red
0.2
Yellow
0.2
Green
0.1
Orange Blue
0.1
?
12. What is the probability that an M & M is blue?
13. What is the probability that an M & M is red or green?
14. What is the probability that an M & M is yellow and orange?
15. What is the probability that an M & M is not brown or blue?
16. Bre can beat Erica in tennis 9% of the time. Erica can swim faster than Bre 8% of the time. What is
the probability that Bre would beat Erica in a tennis match and in a swimming race?
17. What assumption are you making in problem 16? Do you think this assumption is valid?
18. Using two dice, what is the probability that you would roll a sum of seven or eleven?
19. Using two dice, what is the probability that you would roll doubles?
20. Using two dice, what is the probability that you would roll a sum of 7 or 11 on the first roll and doubles
on the second roll?
21. What assumption are you making in problem 20? Do you think this assumption is valid?
22. Using two dice, what is the probability that you would roll a sum of 7 or 11 that is also doubles?
23. What is the union of two events?
24. What is an intersection of two events?
25. How can we test independence?
26. Make a Venn diagram for the following situation:
45% of kids like Barney
25% of kids like Blue
55% of kids like Pooh
15% of kids like Blue and Pooh
25% of kids like Barney and Pooh
5% of kids Barney, Blue, and Pooh
5% of kids like Blue but not Barney or Pooh
27. A dartboard has a circle with a 20-inch diameter drawn inside a 2-foot square. What is the probability
that a dart lands inside the circle given that it at least lands inside the square? (Assume a random
trial here.)
28. Give an example of a discrete random variable.
29. Give an example of a continuous random variable.
30. Make a probability histogram of the following grades on a four-point scale:
Grade
Probability
0
0.05
1
0.28
2
0.19
3
0.32
4
0.16
31. Using problem 30, what is P(X > 2)?
32. Using problem 30, what is P(X > 2)?
33. What is a uniform distribution? Draw a picture.
34. In a uniform distribution, what is P(0.2 < X < 0.6)?
35. In a uniform distribution, what is P(0.2 < X < 0.6)?
36. How do your answers to problems 30-34 demonstrate a difference between continuous and discrete
random variables?
37. Normal distributions are (continuous or discrete).
38. Expected value is another name for _____.
39. Calculate the expected value of the grades in problem 30.
40. Calculate the variance of the grades in problem 30.
41. Calculate the standard deviation of the grades in problem 30.
42. What is the law of large numbers?
43. If I sell an average of 5 books per day and 7 CDs per day, what is the average number of items I sell
per day?
44. If I charge $2 per book and $1.50 per CD in problem 43, what is my average amount of income per
day?
45. Before you can use the rules for variances you must make sure the variables are _____.
Use the following situation: For F Period, the class average was 80 with a standard deviation of 10. For
G Period, the class average was 70 with a standard deviation of 12.
46. What is the average for the two tests added together?
47. What is the standard deviation for the two tests added together?
48. What is the difference in the test averages?
49. What is the standard deviation for the difference in the test averages?
50. If I cut the test scores for G period in half and add 50, what is the new average?
51. What is the new standard deviation for G’s tests in problem 50?
52. If I add 7 points to every F period test score, what is the new standard deviation?
53. If I multiply every F period score by 2 and subtract 80, what is the new mean?
54. If I multiply every F period test score by 2 and subtract 80, what is the new standard deviation?
Statistics Review Chapter 8 and Miscellaneous
55. What are the four conditions of a binomial distribution?
56. What are the four conditions of a geometric distribution?
Use the following situation for questions 57-64: The probability that a child born to a certain set of parents
will have blood type AB is 25%.
57. The parents have four children. X is the number of those children with blood type AB. Is this
binomial or geometric?
58. Using the situation in problem 57, calculate P(X = 2).
59. Using the situation in problem 57, calculate P(X < 3).
60. Using the situation in problem 57, calculate P(X > 1).
61. Using the situation in problem 57, calculate P(1 < X < 3).
62. Using the situation in problem 57, calculate P(2 < X < 4).
63. What is the mean of the situation in problem 57?
64. What is the standard deviation of the situation in problem 57?
65. The parents have children until they have a child with type AB blood. X is the number of children they
have to give birth to one with type AB blood. Is this binomial or geometric?
66. Using the situation in problem 65, calculate P(X = 1).
67. Using the situation in problem 65, calculate P(X < 2).
68. Using the situation in problem 65, calculate P(X > 5).
69. Using the situation in problem 65, calculate P(2 < X < 4).
70. Using the situation in problem 65, calculate P(2 < X < 5).
71. What is the mean of the situation in problem 65?
72. Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the
average life expectancy to reach 100, 18% of people would have to live to 120. What standard
deviation is he assuming for this statement to make sense? (Assume normal distribution.)
73. Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the
mean weight if 85% of the cucumbers weigh less than 16 ounces? (Assume normal distribution.)
74. If 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is
the mean weekly expenditure and what is the standard deviation? (Assume normal distribution.)
For problems 75-79 consider the process of a drawing a card from a standard deck and replacing it. Let
A be drawing a heart, B be drawing a king, and C be drawing a spade.
75. Are the events A and B disjoint? Explain.
76. Are the events A and B independent? Explain.
77. Are the events A and C disjoint? Explain.
78. Are the events A and C independent? Explain.
79. Give me an example of two events that are disjoint and independent.